A numerical method for the fractional Fitzhugh–Nagumo monodomain model

A fractional FitzHugh–Nagumo monodomain model with zero Dirichlet boundary conditions is presented, generalising the standard monodomain model that describes the propagation of the electrical potential in heterogeneous cardiac tissue. The model consists of a coupled fractional Riesz space nonlinear reaction-diffusion model and a system of ordinary differential equations, describing the ionic fluxes as a function of the membrane potential. We solve this model by decoupling the space-fractional partial differential equation and the system of ordinary differential equations at each time step. Thus, this means treating the fractional Riesz space nonlinear reaction-diffusion model as if the nonlinear source term is only locally Lipschitz. The fractional Riesz space nonlinear reaction-diffusion model is solved using an implicit numerical method with the shifted Grunwald–Letnikov approximation, and the stability and convergence are discussed in detail in the context of the local Lipschitz property. Some numerical examples are given to show the consistency of our computational approach.

PySSM : a Python module for Bayesian inference of linear Gaussian state space models

PySSM is a Python package that has been developed for the analysis of time series using linear Gaussian state space models (SSM). PySSM is easy to use; models can be set up quickly and efficiently and a variety of different settings are available to the user. It also takes advantage of scientific libraries Numpy and Scipy and other high level features of the Python language. PySSM is also used as a platform for interfacing between optimised and parallelised Fortran routines. These Fortran routines heavily utilise Basic Linear Algebra (BLAS) and Linear Algebra Package (LAPACK) functions for maximum performance. PySSM contains classes for filtering, classical smoothing as well as simulation smoothing.

Negative space and positive environment : mapping opportunities for urban resilience

Cities have long held a fascination for people – as they grow and develop, there is a desire to know and understand the intricate interplay of elements that makes cities ‘live’. In part, this is a need for even greater efficiency in urban centres, yet the underlying quest is for a sustainable urban form. In order to make sense of the complex entities that we recognise cities to be, they have been compared to buildings, organisms and more recently machines. However the search for better and more elegant urban centres is hardly new, healthier and more efficient settlements were the aim of Modernism’s rational sub-division of functions, which has been translated into horizontal distribution through zoning, or vertical organisation thought highrise developments. However both of these approaches have been found to be unsustainable, as too many resources are required to maintain this kind or urbanisation and social consequences of either horizontal or vertical isolation must also be considered. From being absolute consumers of resources, of energy and of technology, cities need to change, to become sustainable in order to be more resilient and more efficient in supporting culture, society as well as economy. Our urban centres need to be re-imagined, re-conceptualised and re-defined, to match our changing society. One approach is to re-examine the compartmentalised, mono-functional approach of urban Modernism and to begin to investigate cities like ecologies, where every element supports and incorporates another, fulfilling more than just one function. This manner of seeing the city suggests a framework to guide the re-mixing of urban settlements. Beginning to understand the relationships between supporting elements and the nature of the connecting ‘web’ offers an invitation to investigate the often ignored, remnant spaces of cities. This ‘negative space’ is the residual from which space and place are carved out in the Contemporary city, providing the link between elements of urban settlement. Like all successful ecosystems, cities need to evolve and change over time in order to effectively respond to different lifestyles, development in culture and society as well as to meet environmental challenges. This paper seeks to investigate the role that negative space could have in the reorganisation of the re-mixed city. The space ‘in-between’ is analysed as an opportunity for infill development or re-development which provides to the urban settlement the variety that is a pre-requisite for ecosystem resilience. An analysis of the urban form is suggested as an empirical tool to map the opportunities already present in the urban environment and negative space is evaluated as a key element in achieving a positive development able to distribute diverse environmental and social facilities in the city.

Stratospheric dust collections : valuable resources for space and atmospheric scientists

Collections of solid particles from the Earths' stratosphere have been a significant part of atmospheric research programs since 1965 [1], but it has only been in the past decade that space-related disciplines have provided the impetus for a continued interest in these collections. Early research on specific particle types collected from the stratosphere established that interplanetary dust particles (IDP's) can be collected efficiently and in reasonable abundance using flat-plate collectors [2-4]. The tenacity of Brownlee and co-workers in this subfield of cosmochemistry has led to the establishment of a successful IDP collection and analysis program (using flat-plate collectors on high-flying aircraft) based on samples available for distribution from Johnson Space Center [5]. Other stratospheric collections are made, but the program at JSC offers a unique opportunity to study well-documented, individual particles (or groups of particles) from a wide variety of sources [6]. The nature of the collection and curation process, as well as the timeliness of some sampling periods [7], ensures that all data obtained from stratospheric particles is a valuable resource for scientists from a wide range of disciplines. A few examples of the uses of these stratospheric dust collections are outlined below.

Introduction : Understanding Connections between Time, Space and the Body

The experiences and constructs of time, space and bodies saturate human discourse—naturally enough, since they are fundamental to existence—yet there has long been a tendency for the terms to be approached somewhat independently, belying the depth of their interconnections. It was a desire to address that apparent shortcoming that inspired this book, and the interdisciplinary meetings from which it was born, the 1st Global Conferences on ‘Time, Space and the Body’ and ‘Body Horror’ held in Sydney in February 2013. Following the lively, often provocative, exchange of ideas throughout those meetings, the writing here crosses conventional boundaries inhabiting everyday life and liminal experiences, across cultures, life circumstances, and bodily states. Through numerous theoretical frameworks and with reference to a variety of media, the authors problematize or deconstruct commonplace assumptions to reveal challenging new perspectives on the diverse cultures and communities which make our world. If there is an overarching theme of this collection it is diversity itself. The writers here come from numerous academic fields, but a good number of them also draw on first-hand cultural production in the arts: photography, sculpture and fine art instillation, for example. Of course, however laudable it might be, there is a potential problem in such diversity: does it produce fruitful dialogue moving toward creative, workable syntheses or simply a cacophony of competing, incomprehensible, barely comprehending voices? To a large degree this depends upon the intellectual, existential ambitions as well as the old-fashioned goodnatured tolerance of both writers and readers. But we hope three unifying characteristics are discernable in the following chapters viewed as a whole: firstly, a genuine concern for the world humans inhabit and the communities they form as bodies in space and time; secondly, an emphasis upon the experience of the human subject, exemplified perhaps by the number of chapters drawing on phenomenology; thirdly, an adventurous, explorative impulse associated with an underlying sense that being, since it is inseparable from the body’s temporality, is always becoming, and here the presence of poststructuralist influences is unmistakable, often explicit. Our challenge as editors has been to present the enormous variety of subjects and views in a way that would render the book coherent and at the same time encourage readers to make explorations themselves into realms they might usually consider beyond their field of interest. To that end we have divided the book into six sections around loosely defined themes, each offering different angles on how time and/or space unfold in and around bodies.

On the order of the fractional Laplacian in determining the spatio-temporal evolution of a space-fractional model of cardiac electrophysiology

Space-fractional operators have been used with success in a variety of practical applications to describe transport processes in media characterised by spatial connectivity properties and high structural heterogeneity altering the classical laws of diffusion. This study provides a systematic investigation of the spatio-temporal effects of a space-fractional model in cardiac electrophysiology. We consider a simplified model of electrical pulse propagation through cardiac tissue, namely the monodomain formulation of the Beeler-Reuter cell model on insulated tissue fibres, and obtain a space-fractional modification of the model by using the spectral definition of the one-dimensional continuous fractional Laplacian. The spectral decomposition of the fractional operator allows us to develop an efficient numerical method for the space-fractional problem. Particular attention is paid to the role played by the fractional operator in determining the solution behaviour and to the identification of crucial differences between the non-fractional and the fractional cases. We find a positive linear dependence of the depolarization peak height and a power law decay of notch and dome peak amplitudes for decreasing orders of the fractional operator. Furthermore, we establish a quadratic relationship in conduction velocity, and quantify the increasingly wider action potential foot and more pronounced dispersion of action potential duration, as the fractional order is decreased. A discussion of the physiological interpretation of the presented findings is made.

Lady Nugent and Tom Cringle on the veranda : early nineteenth century observations on a Caribbean architectural feature

This study of the veranda as seen through the eyes of Lady Maria Nugent and Michael Scott, alias Tom Cringle, clearly demonstrates the important role that the piazza, as it was then more commonly known, played in the life of early nineteenth century Caribbean colonial society. The popularity of the veranda throughout the region, in places influenced by different European as well as African cultures, and among all classes of people, suggests that the appeal of this typical feature was based on something more than architectural fashion. A place of relative comfort in hot weather, the veranda is also a space at the interface of indoors and outdoors which allows for a wide variety of uses, for solitary or small or large group activities, many of which were noted by Nugent and Scott. Quintessentially, the veranda is a place in which to relax and take pleasure, not least of which is the enjoyment of the prospect, be it a panoramic view, a peaceful garden or a lively street scene. Despite the great changes in the nature of society, in the Caribbean and in many other parts of the world, the veranda and related structures such as the balcony continue to play at least as important a role in daily life as they did two centuries ago. The veranda of today’s Californian or Australian bungalow, and the balcony of the apartment block in the residential area of the modern city are among the contemporary equivalents of the lower and upper piazzas of Lady Nugent’s and Tom Cringle’s day.

Numerical approximation of a fractional-in-space diffusion equation (II) - with nonhomogeneous boundary conditions

In this paper, a space fractional di®usion equation (SFDE) with non- homogeneous boundary conditions on a bounded domain is considered. A new matrix transfer technique (MTT) for solving the SFDE is proposed. The method is based on a matrix representation of the fractional-in-space operator and the novelty of this approach is that a standard discretisation of the operator leads to a system of linear ODEs with the matrix raised to the same fractional power. Analytic solutions of the SFDE are derived. Finally, some numerical results are given to demonstrate that the MTT is a computationally e±cient and accurate method for solving SFDE.